1. Copyright © 2002 Cycorp The Basics Arity Argument Types Second-Order Predicates More on Functions Predicates and Denotational Functions

2. Copyright © 2002 Cycorp Argument Types The types of arguments a predicate or function requires. While this is a term : (#$MotherFn #$HillaryClinton) There’s something odd about : (#$MotherFn #TheWhiteHouse) The White House is not the kind of thing that can have a mother. #$TheWhiteHouse (unlike #$HillaryClinton ) is not an appropriate type of argument for #$MotherFn We can state in CycL the type(s) of arguments appropriate for a given predicate or function....

3. Copyright © 2002 Cycorp Argument Types Argument types can be specified two ways #$arg[N]Isa : states what the Nth argument must be an instance of #$arg[N]Genl : states what the Nth argument must be a specialization of

4. Copyright © 2002 Cycorp Argument Types Example 1 (#$arg1Isa #$mother #$Animal) (#$arg2Isa #$mother #$FemaleAnimal) Thus, (#$mother #$ChelseaClinton #$HillaryClinton) is a well-formed sentence because : (#$isa #$ChelseaClinton #$Animal) and (#$isa #$HillaryClinton #$FemaleAnimal)

5. Copyright © 2002 Cycorp Argument Types Example 2 (#$arg1Isa #$TransportViaFn #$ExistingObjectType) (#$arg1Genl #$TransportViaFn #$SolidTangibleThing) Thus, (#$TransportViaFn #$Automobile) is a well-formed NAT because #$Automobile is both: an instance of #$ExistingObjectType and a specialization of #$SolidTangibleThing.

6. Copyright © 2002 Cycorp Argument Types A relation must be applied to arguments that meet its argument type specifications for the result to be semantically well- formed. (#$MotherFn #$TheWhiteHouse) is semantically malformed. (#$MotherFn #$HillaryClinton) is semantically well- formed. Cf. A relation must be applied to the proper number of arguments for its arity for the result to be syntactically well-formed.

7. Copyright © 2002 Cycorp Examples of Predicate Use Given this information : (#$isa #$objectHasColor #$BinaryPredicate) (#$arg1Isa #$objectHasColor #$SpatialThing-Localized) (#$arg2Isa #$objectHasColor #$Color) Are these well-formed formulas ? (#$objectHasColor #$GoldenRetriever #$TanColor $GoldColor) (#$objectHasColor #$Emerald-Gem #$GreenColor) (#$objectHasColor #$TheWhiteHouse #$WhiteColor) (#$objectHasColor #$TheWhiteHouse #$PinkColor)

8. Copyright © 2002 Cycorp Examples of Predicate Use Given this information : (#$isa #$objectHasColor #$BinaryPredicate) (#$arg1Isa #$objectHasColor #$SpatialThing-Localized) (#$arg2Isa #$objectHasColor #$Color) Are these well-formed formulas ? (#$objectHasColor #$GoldenRetriever #$TanColor $GoldColor) (#$objectHasColor #$Emerald-Gem #$GreenColor) (#$objectHasColor #$TheWhiteHouse #$WhiteColor) (#$objectHasColor #$TheWhiteHouse #$PinkColor)

9. Copyright © 2002 Cycorp Examples of Predicate Use Given this information : (#$isa #$objectHasColor #$BinaryPredicate) (#$arg1Isa #$objectHasColor #$SpatialThing- Localized) (#$arg2Isa #$objectHasColor #$Color) Are these well-formed formulas ? (#$objectHasColor #$GoldenRetriever #$TanColor $GoldColor) (#$objectHasColor #$Emerald-Gem #$GreenColor) (#$objectHasColor #$TheWhiteHouse #$WhiteColor) (#$objectHasColor #$TheWhiteHouse #$PinkColor)

10. Copyright © 2002 Cycorp Summary Each predicate and function is defined to use arguments of particular types Argument types can be specified in two ways #$arg[N]Isa #$arg[N]Genl A relation must be applied to arguments that meet its argument type specifications if the result is to be semantically well-formed